The present invention relates to a radar system which predicts the position, velocity, and acceleration of a severely maneuvering target for controlling the aiming of a implement, such as a weapon or camera, for example, at such target.
In a typical radar system, pulses are transmitted through an antenna at a predetermined repetition rate toward a target. The time of reception of the transmitted pulses by the antenna provides information as to the range or distance of the target from the antenna (R) and the rate of change of the range of the target (R). The velocity of the target (V.sub.T) may be determined by combining ownship velocity with the doppler frequency shift between the transmitted pulse and the received echo pulse.
For a radar system mounted on an aircraft, there are a number of different Cartesian coordinate systems involved in the tracking of a target and the pointing of a weapon or camera at a target. An earth or geographic coordinate system extends along north, east, and down axes (N, E and D) respectively. An aircraft coordinate system extends along dead-ahead, right, and down axes (X, Y and Z) from the nose of the aircraft, respectively; and a line of sight or antenna coordinate system extends along axes in the direction that the antenna is pointing (i), orthogonally to the right (j), and down from such direction (k). These coordinate systems may be utilized in the tracking operation of the antenna and the pointing of a weapon or camera at a target. Thus, vector information can be obtained relative to such coordinates to track the target with the antenna; and also point an implement at such target. For example, signals may be generated that are representative of the attitude of the aircraft relative to the horizon; that is, nose up or nose down, as the case may be, as well as signals representative of the velocity of the aircraft in its true direction. These signals, as well as tracking error signals of the antenna are input to and operated upon by a digital computer that calculates the various output signals for positioning the antenna to maintain its track on the target; and in some applications to operate a weapon control unit for directing a weapon or camera at a maneuvering target. In the mechanization of the system, a high speed digital computer may be utilized that operates upon the input signals every 0.02 seconds, for example. The new range measurement signals may be read by the computer every 0.04 of a second and the angle measurements are operated upon by the computer every 0.04 seconds during alternate cycles of calculation. Each calculation may be output to the antenna at a rate of one every 0.005 of a second for controlling its position, for example, and the output signals to control the weapon control system may occur anywhere from 0.005 to 0.04 seconds, for example, as desired.
From the input information, estimates of the target position are generated at predetermined fractions of a second; and such target position estimate signals, which are determined from the last estimated position, target velocity and target acceleration estimation signals, are then utilized to direct toward, or maintain the antenna on the moving target; and, may be also utilized to control the pointing of an implement at the target.
An optimal estimating system that is well suited for program implementation in a high speed digital computer is the estimator known as a Kalman filter. The Kalman filter is well known in the literature and may be defined as an optimal recursive filter that is based on state space and time domain formulations.
In such estimator, the current calculated estimate of acceleration is determined by conventional calculations of a predetermined number of past acceleration estimates. For example, assuming that there are fifty estimates of acceleration calculated evey second and a time constant TTC of three seconds is utilized, then one hundred fifty of such estimations are utilized in calculating the present or current acceleration estimation of the target. It is well known that acceleration and deceleration builds up and decays more or less rapidly for different types of targets; and that different time constants TTC may be used for different targets. Thus, for relatively slowly accelerating targets a TTC of ten or fifteen seconds may be used to obtain the required estimated accuracy. For rapidly accelerating targets, a shorter TTC is required in the neighborhood of one to three seconds, for example in order to provide an accurate estimation. In each such current estimate of acceleration, each one of the previous calculations utilized, are decremented a predetermined amount. For example, for a three second time constant with fifty calculations per second, the 150 calculations are decremented by 1/150th of the gain factor of the estimator, which of course provides less weight to each previous calculation of acceleration until each calculation is decremented to zero.
High speed aircraft having the capability of rapid turns and thus rapid changes in acceleration has rendered the optimal estimation of position, particularly for weapon control, difficult. In the generation of the acceleration output estimation signal, it has been found that it is necessary to decrement or bleed off the previous calculations of acceleration at a relatively rapid rate in order to provide for an accurate estimate. Such decrementing or bleeding of the signal may be accomplished every 0.02 seconds, for example, as previously mentioned, by multiplying each previously calculated or obsolete estimate of acceleration by 1-(0.02/TTC), where TTC is a target time constant, and 0.02 corresponds to the time interval since the last calculated acceleration estimate. For example, if the last calculated acceleration were 4 G's, the time constant TTC might be 4, for 5 G's, the TTC would be 5, and so on. Since the resulting number is less than 1, each subsequent calculation would tend to drive the previous acceleration estimate to zero. In some instances, particularly for utilizing the acceleration estimate for weapon control, the output signals may be updated more or less frequently than the output signals to the antenna. The penalty exacted for decrementing or decaying the old or obsolete acceleration estimates relatively rapidly is that the magnitude of the acceleration estimate for severely maneuvering targets never achieves full value. Typically, 50 to 80% of full value is achieved. If the decrementing of the acceleration estimate is decreased, so as to extend the time constant TTC to 10 or 20 seconds, for example, the full value or magnitude of the acceleration estimate may be achieved but the accuracy of the system would be further decreased in attempting to track targets having a rapid change of acceleration.
Thus, it is desirable to provide an improved radar system where the estimated acceleration output signal is corrected to provide for a more accurate estimation of position for severely maneuvering targets.